Finite Group Databasebeta

← #16945027

Subgroups — #16945027

Order 4352.

388 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534550C211yesmaximal, characteristic
2#14527118C211yesmaximal, characteristic
3#14526789C214yesmaximal, complemented
4C17×#1822C211yesmaximal, characteristic
5C2×#10587555C411yescharacteristic
6C2×#10587610—21no—
7#11762866—21no—
8#11762739—21no—
9#11762739C2212yes—
10#11762734—21no—
11#11762734C412yes—
12#11762715—21no—
13#11762675C411yescharacteristic
14#11762535C2212yes—
15#11762533—21no—
16C2×C17×#117C2211yescharacteristic
17C17×#407—21no—
18C17×#343—21no—
19C17×#343C2212yes—
20C23×C4×C17D411yescharacteristic
21C22×Dic34—21no—
22C2×M16×C17—22no—
23C17×#117—41no—
24C17×#117—41no—
25C2×C4⋊C4×C17D411yescharacteristic
26C2×C4⋊C4×C17C2311yescharacteristic
27C2×C22⋊C4×C17C2×C411yescharacteristic
28C2×C22⋊C4×C17D411yescharacteristic
29C2×C42×C17C2×C411yescharacteristic
30C2×C42×C17D411yescharacteristic
31C2×C22⋊Dic17—22no—
32C2×C4⋊Dic17—21no—
33C2×C4⋊Dic17—21no—
34C2×C4⋊Dic17C2×C412yes—
35#10587610—44no—
36C2×#63225—22no—
37#10587555—41no—
38#10587555—41no—
39C17×C22⋊C8—41no—
40C17×C22⋊C8—41no—
41#10587502—22no—
42#10587502—21no—
43#10587502—22no—
44#10587502C2×C412yes—
45C22⋊#3622—22no—
46C4⋊#3622—41no—
47#10587474—41no—
48C24×C17C22⋊C411yescharacteristic
49C22×C4×C17—21no—
50C22×C4×C17—21no—
51C22×C4×C17—22no—
52C22×C4×C17—41no—
53C22×C4×C17C22⋊C411yescharacteristic
54C22×C4×C17C22⋊C411yescharacteristic
55C22×C4×C17C22⋊C411yescharacteristic
56C22×C4×C17C22×C411yescharacteristic
57C22×C4×C17C2×D411yescharacteristic
58C22×C4×C17C2×D411yescharacteristic
59C22×Dic17—22no—
60C22×Dic17—22no—
61C2×Dic34—42no—
62C2×Dic34—42no—
63C2×Dic34—41no—
64C2×Dic34—41no—
65M16×C17—42no—
66M16×C17—42no—
67C2×C8×C17—42no—
68C4⋊C4×C17—41no—
69C4⋊C4×C17—41no—
70C22⋊C4×C17—41no—
71C22⋊C4×C17—41no—
72C42×C17—21no—
73C42×C17—21no—
74C42×C17—21no—
75C42×C17—21no—
76C22⋊Dic17—44no—
77C4⋊Dic17—42no—
78C4⋊Dic17—42no—
79C4⋊Dic17—42no—
80#63225—44no—
81C2×#3622—42no—
82#11807—171nomaximal, Sylow
83C23×C17—21no—
84C23×C17—21no—
85C23×C17—21no—
86C23×C17—41no—
87C23×C17—41no—
88C23×C17C2×C22⋊C411yescharacteristic
89C2×C4×C17—21no—
90C2×C4×C17—21no—
91C2×C4×C17—21no—
92C2×C4×C17—21no—
93C2×C4×C17—21no—
94C2×C4×C17—21no—
95C2×C4×C17—21no—
96C2×C4×C17—21no—
97C2×C4×C17—42no—
98C2×C4×C17—42no—
99C2×C4×C17—41no—
100C2×C4×C17—41no—
101C2×C4×C17—41no—
102C2×C4×C17—41no—
103C2×C4×C17#9911yescharacteristic
104C2×C4×C17#9911yescharacteristic
105C2×C4×C17AGL(1,ℤ/8)12yes—
106C2×Dic17—42no—
107C2×Dic17—42no—
108C2×Dic17—42no—
109C2×Dic17—42no—
110C2×Dic17—42no—
111C2×Dic17—42no—
112Dic34—82no—
113Dic34—82no—
114C8×C17—82no—
115#3622—82no—
116#2621—171no—
117#1822D1711yescharacteristic
118#1464—171no—
119#1346—174no—
120C22×C17—21no—
121C22×C17—21no—
122C22×C17—42no—
123C22×C17—41no—
124C22×C17—41no—
125C22×C17—41no—
126C22×C17—81no—
127C22×C17C2×#9911yescharacteristic
128C22×C17#41811yescharacteristic
129C22×C17#42111yescharacteristic
130C4×C17—22no—
131C4×C17—21no—
132C4×C17—21no—
133C4×C17—41no—
134C4×C17—41no—
135C4×C17—41no—
136C4×C17—41no—
137Dic17—82no—
138Dic17—82no—
139C2×C4⋊Q8—171no—
140C2×C22⋊Q8—341no—
141C2×#117C2×D1711yescharacteristic
142#432—341no—
143#407—21no—
144#398—172no—
145#398—341no—
146#397—172no—
147#397—341no—
148#391—341no—
149#382—171no—
150#343—21no—
151#343C2×D1712yes—
152#324—172no—
153#323—341no—
154C2×C17—21no—
155C2×C17—21no—
156C2×C17—81no—
157C2×C17#151011yescharacteristic
158C2×C17#212311yescharacteristic
159C2×C17#213511yescharacteristic
160C22×Q8—341no—
161C23×C4C22⋊D1711yescharacteristic
162C2×M16—22no—
163C4⋊Q8—681no—
164C4⋊Q8—681no—
165C22⋊Q8—684no—
166#117—41no—
167#117—41no—
168C2×C4⋊C4—172no—
169C2×C4⋊C4—342no—
170C2×C4⋊C4—341no—
171C2×C4⋊C4—341no—
172C2×C4⋊C4C22⋊D1711yescharacteristic
173C2×C4⋊C4C22×D1711yescharacteristic
174C2×C22⋊C4—342no—
175C2×C22⋊C4C4×D1711yescharacteristic
176C2×C22⋊C4D6811yescharacteristic
177C2×C42C4×D1711yescharacteristic
178C2×C42D6811yescharacteristic
179C4⋊C8—681no—
180C22⋊C8—41no—
181C22⋊C8—41no—
182C22⋊C8—342no—
183#97—681no—
184#95—172no—
185#95—342no—
186#95—341no—
187#95—342no—
188C17#1180711yescharacteristic, complemented, Sylow
189C24#6322711yescharacteristic
190C2×Q8—682no—
191C2×Q8—682no—
192C2×Q8—681no—
193C2×Q8—681no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—22no—
197C22×C4—41no—
198C22×C4—342no—
199C22×C4—342no—
200C22×C4#6322711yescharacteristic
201C22×C4#6322711yescharacteristic
202C22×C4#6322711yescharacteristic
203C22×C4C2×C4×D1711yescharacteristic
204C22×C4C2×D6811yescharacteristic
205C22×C4C2×C22⋊D1711yescharacteristic
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—682no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—682no—
213C4⋊C4—682no—
214C4⋊C4—682no—
215C4⋊C4—684no—
216C22⋊C4—41no—
217C22⋊C4—41no—
218C22⋊C4—684no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C23—21no—
224C23—21no—
225C23—21no—
226C23—41no—
227C23—41no—
228C23C2×#6322711yescharacteristic
229Q8—1362no—
230Q8—1362no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4—41no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—682no—
246C2×C4—682no—
247C2×C4—682no—
248C2×C4—682no—
249C2×C4—682no—
250C2×C4—682no—
251C2×C4#1058747711yescharacteristic
252C2×C4#1058747711yescharacteristic
253C2×C4#1058763512yes—
254C8—82no—
255C8—1362no—
256C22—21no—
257C22—21no—
258C22—42no—
259C22—41no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22C2×#1058747711yescharacteristic
264C22#1176281311yescharacteristic
265C22#1176282711yescharacteristic
266C4—22no—
267C4—21no—
268C4—21no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—41no—
273C4—1362no—
274C4—1362no—
275C2—21no—
276C2—21no—
277C2—81no—
278C2#1452731211yescharacteristic
279C2#1453043911yescharacteristic
280C2#1453047811yescharacteristic
subgroupG/H
centerC22C2×#10587477
commutatorC22×C4×C17C22×C4
FrattiniC2×C4⋊C4C22×D17
FittingC17×#1822C2
socleC22×C17C2×#99
prime radicalC24×C17C22⋊C4
cosocleC2×C4⋊C4×C17C23
hypercenter#1822D17
hypocenterC17#11807
LCSG ▷ C22×C4×C17 ▷ C23×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1822

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. #14526789C2semidirect
188. C17#11807semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145345502
#145271182
#145267892
C17×#18222
#1180717